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Mathematical Foundations and Challenges for GeoAI
Conference proceeding   Open access   Peer reviewed

Mathematical Foundations and Challenges for GeoAI

Zhangyu Wang, Peng Luo and Gengchen Mai
Geography According to Foundation Models, Vol.422, pp.51-74
05/21/2026
DOI: 10.3233/FAIA260469
url
https://doi.org/10.3233/FAIA260469View
Published (Version of record) Open Access

Abstract

GeoAI has advanced rapidly, but its reliability depends on whether geographic structure is treated as a mathematical constraint rather than a data attribute. This chapter develops a unified mathematical roadmap from classical spatial modeling to modern GeoAI. We first explain why spatial data are special, emphasizing dependence, heterogeneity, geometric distortion, and sampling imbalance, all of which challenge standard i.i.d.-based learning assumptions. We then revisit two pre-GeoAI foundations: geostatistical models for prediction with uncertainty and spatial regression models for mechanism-oriented interpretation. Building on these foundations, we show how GeoAI can be reformulated through three coupled components: spatial loss functions in optimization, spatial representation learning in model design, and spatially explicit uncertainty quantification in evaluation. We further compare major uncertainty paradigms for GeoAI, including Bayesian, bootstrap/ensemble, and conformal approaches, and discuss why localized calibration (e.g., GeoCP) is critical under spatial shift. Overall, the chapter connects traditional GIScience mathematics with contemporary GeoAI and provides a principled basis for building trustworthy, interpretable, and uncertainty-aware geospatial AI systems.
 conformal prediction GeoAI geostatistics spatial regression spatial representation learning uncertainty quantification

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